Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 7x + 4$ and $ BC = 4x + 25$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {7x + 4} = {4x + 25}$ Solve for $x$ $ 3x = 21$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 7({7}) + 4$ $ BC = 4({7}) + 25$ $ AB = 49 + 4$ $ BC = 28 + 25$ $ AB = 53$ $ BC = 53$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {53} + {53}$ $ AC = 106$